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Unformatted text preview: Chapter 8 Interval Estimation Outline: Interval Estimation of a Population Mean Large Sample Case Small Sample Case Determining the Sample Size Interval Estimation of Population Proportion Interval Estimation of a Population Mean: Large-Sample Case (I) Sampling Error (II) Probability Statement about the Sampling Error (III) Constructing an Interval Estimate: Large-Sample Case with Known (IV) Calculating an Interval Estimate: Large-Sample Case with Unknown (I). Sampling Error: Sampling error: The absolute value of the difference between an unbiased point estimate and the population parameter. 1 For the case of a sample mean estimating a population mean, the sampling error = - x Margin of Error: The upper limit on the sampling error. Motivation for Interval Estimation: Population mean ( ) is usually unknown. In practice, the value of the sampling error cannot be determined exactly because the population mean is unknown. Therefore, the sampling distribution of x can be used to make probability statements about the sampling error. Interval Estimation: An interval estimate of a population parameter is constructed by subtracting and adding a value, called the margin of error , to a point estimate, i.e., x Margin of Error. From last chapter, we know how to compute =&gt; 2 ) ( k X k P - - Intervals and Level of Confidence: Interval extend from x z x 2 /- to x z x 2 / + We are 100(1- )% confident that the interval constructed from x z x 2 /- to x z x 2 / + will include the population mean . 1. This interval is established at the 100(1- )% confidence level . 2. The value (1- ) is referred to as the confidence coefficient . 3. The interval estimate x z x 2 / is called a 100(1- )% confidence interval (CI). What are the factors affecting intervals? 3 2 / 2 / Sampling Distribution 1- of all values x x 100(1 - ) % of intervals contain . 100 % do not. Example: A simple random sample of 50 items resulted in a sample mean of 32 and a sample standard deviation of 6....
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